Optimisation and Operations Research - Lecture 14: ILPs in Matlab and AMPL

26 Pages·2017·0.35 MB·English

Optimisation and Operations Research
Lecture 14: ILPs in Matlab and AMPL
Matthew Roughan
<[email protected]>
http:
//www.maths.adelaide.edu.au/matthew.roughan/notes/OORII/
SchoolofMathematicalSciences,
UniversityofAdelaide
September 12, 2019
Section 1
Integer Programming: Matlab
MatthewRoughan(SchoolofMathematicalSciences, UniversityOoOfRAIdIelaide) September12,2019 2/25
Matlab
intlinprog
Similar to the linprog command in Matlab for linear programs that have
variables which can take on real solutions, there exists a command
intlinprog for those linear programs that are also constrained to have
variables to be integer, i.e., which can only take on the values 0 or 1.
That is, intlinprog solves binary linear programming problems of the form

A x ≤ b

minfTx, such that A x = b
eq eq
x  some x integer
i
where, f, b, and b are vectors, A and A are matrices, and some of the
eq eq
the variables are required to be integers.
MatthewRoughan(SchoolofMathematicalSciences, UniversityOoOfRAIdIelaide) September12,2019 3/25
MATLAB intlinprog example
Commands: for Binary program below
> f = [-9; -5; -6; -4];
> A = [6,3,5,2; 0,0,1,1; -1,0,1,0; 0,-1,0,1];
> b = [9; 1; 0; 0];
> Aeq = [];
> beq = [];
> intcon = [1,2,3,4];
> ub = ones(4,1);
> lb = zeros(4,1);
> x = intlinprog(f,intcon,A,b,Aeq,beq,lb,ub)
Output:
x = 1
1
0
0
MatthewRoughan(SchoolofMathematicalSciences, UniversityOoOfRAIdIelaide) September12,2019 4/25
When to use intlinprog
Don’t cheat
(cid:73) use this to check solutions
(cid:73) but solve them the way required in your assignments
Yes, you can use it in your project
(cid:73) but display understanding
(cid:73) show alternatives
In general
(cid:73) you still need to construct matrices and vectors which is awkward
(cid:73) you need to write every constraint, even if they fit a pattern
(cid:73) you still need explicit (closed form) constraints and objective functions
(cid:73) Matlab doesn’t tell you much about how it does it, and what its
limitations are
(cid:70) we know the problem might be NP-complete, so this could be an issue
MatthewRoughan(SchoolofMathematicalSciences, UniversityOoOfRAIdIelaide) September12,2019 5/25
Section 2
AMPL
MatthewRoughan(SchoolofMathematicalSciences, UniversityOoOfRAIdIelaide) September12,2019 6/25
Practical Optimisation
Matlab is all very well, but what do real optimisers do?
MatthewRoughan(SchoolofMathematicalSciences, UniversityOoOfRAIdIelaide) September12,2019 7/25
Mathematical Modelling Languages
There are computer languages designed specifically for optimisation
(cid:73) they allow natural expression of LPs, etc.
(cid:73) they link to multiple backends to solve the problem
(cid:73) they separate the model from the data
(cid:73) they link to other tools, e.g., databases, spreadsheets, ...
(cid:73) support reuse
Common examples:
(cid:73) AMPL
(cid:73) GAMS
(cid:73) AIMMS
(cid:73) MPS (not really a modelling language, but is used for standard input)
(cid:73) ...
MatthewRoughan(SchoolofMathematicalSciences, UniversityOoOfRAIdIelaide) September12,2019 8/25
AMPL = A Mathematical Programming Language
Why AMPL?
(cid:73) I like it
(cid:73) it’s one of the most commonly used (Neos says 59%)
(cid:73) lots of backends
(cid:73) free student version
History
(cid:73) designed 1985 by Robert Fourer, David Gay and Brian Kernighan
(cid:73) 2003 AMPL Optimization LLC
(cid:73) 2012 INFORMS Impact Prize
MatthewRoughan(SchoolofMathematicalSciences, UniversityOoOfRAIdIelaide) September12,2019 9/25
Resources
The AMPL Book, “AMPL: A Modelling Language for Mathematical
Programming”, R.Fourer, D.M.Gay and B.W.Kernighan
(cid:73) Online http://ampl.com/resources/the-ampl-book/
Other tutorials
(cid:73) www.ieor.berkeley.edu/~atamturk/ieor264/samples/ampl/
ampldoc.pdf
Download your own (student) copy of AMPL from
(cid:73) AMPL http://ampl.com/try-ampl/download-a-free-demo/
(cid:73) backends from the same place or others
(cid:70) there are other backends (we are using lpsolve, and I notice they don’t
have a direct link to this anymore).
Online solver NEOS http://www.neos-server.org/neos/
https://neos-server.org/neos/solvers/lp:
Gurobi/AMPL.html
MatthewRoughan(SchoolofMathematicalSciences, UniversityOoOfRAIdIelaide) September12,2019 10/25